FFAG as a phase rotator for the PRISM project A. Sato, M. Aoki, Y. Arimoto, Y. Kuno, M. Yoshida, Osaka University S. Machida, Y. Mori, C. Ohmori, T. Yokoi, K. Yoshimura, KEK Y. Iwashita, Kyoto ICR S. Ninomiya, RCNP
Physics motivation Search for the Lepton Flavor Violating Process One of the important particle physics topics achievable with PRISM is a search for lepton-flavor violating muon rare processes. Lepton flavor violation attracts much attention, theoretically and experimentally, since it would have a large discovery potential to new physics beyond the Standard Model, for instance supersymmetric extension to the Standard Model. An example of proposed experiments of such at PRISM is a search for μ −− e − conversion process in a muonic atom at a sensitivity of 10^-18. A negative muon stopped µ → e γ - 2 1 0 in some material : µ → eee µ A → eA - 4 1 0 Upper limits of Branching Ratio 0 → µ e K L nucleus µ − + → π µ e K - 6 1 0 muon decay in orbit nuclear muon capture - 8 − + ( A , Z ) → ν µ + ( A , Z − 1) − → e 1 0 − νν µ µ - 1 0 1 0 µ − + ( A , Z ) → e − + ( A , Z ) Sensitivities are superb in muon neutrinoless muon nuclear capture - 1 2 1 0 systems (= m-e conversion) History of LFV Search limits physics beyond the Standard Model - 1 4 1 0 Future experiment will cover most 1940 1950 1960 1970 1980 1990 2000 of parameter space with PRISM Y e a r
Requirement to a μ beam for next-gene. experiment High Intensity The potential sensitivity achievable in searches for rare processes is ultimately limited by the number of muons available. The muon beam intensity of 1011 − 1012 μ − /sec should be required, yielding about more than 1020 μ − per year. High Purity Beam contaminations are necessary to be removed, to reduce any background associated with them. It is already shown that the past experiments like SINDRUM-II have already seen a background event just above the signal region, and they suspect that it comes from pion contamination in a beam through radiative pion capture. Therefore, it is the most important to reduce pion contamination in a beam. Narrow Energy Width Narrow energy spread of the beam will allow a thin muon stopping target to improve the momentum resolution of e − detection, which is limited by energy loss in the muon stopping target. High Resolution Spectrometer To improve the intrinsic momentum resolution in an e − spectrometer, it is critical to construct a thin tracking chamber system. super muon source = PRISM
PRISM Phase Rotated Intense Slow Muon source PRISM is a project to provide a Anticipated PRISM beam design characteristics dedicated source of a high intensity muon beam with narrow energy- spread and small beam 10^11-10^12 μ /sec muon intensity contamination. PRISM stands for “Phase Rotated Intense Slow Muon source”. The aimed beam intensity kinetic energy 20MeV is 10^11 − 10^12 μ ±/sec, four orders of magnitude higher than that available at present. It is achieved energy spread +-(0.5-1.0)MeV by a large solid-angle pion capture with a high solenoid magnetic field. Narrow energy spread can be beam repetition 100-1000Hz achieved by phase rotation, which accelerates slow muons and decelerates fast muons by a radio pion contamination < 10^-18 frequency (RF) field. The pion contamination in a muon beam can be removed by a long flight path in PRISM so that most of pions decay out.
PRISM Layout Pion capture section The highest beam intensity in the world could be achieved by large-solid angle capture of pions at their production. Decay section π − μ decay section consisting of a 10-m long superconducting solenoid magnet. Phase rotator to make the beam energy spread narrower. To achieve phase rotation, a fixed-field alternating gradient synchrotron (FFAG) is considered to be used. FFAG advantages: synchrotron oscillation need to do phase rotation large momentum acceptance necessary to accept large momentum distribution at the beginning to do phase rotation large transverse acceptance muon beam is broad in space
Phase rotation Phase rotation is a method to achieve a beam of narrow energy spread. The principle of phase rotation is to accelerate slow muons and decelerate fast muons by a strong radio- frequency (RF) electric field, in order to yield narrow longitudinal momentum spread. By phase rotation, the initial time spread is converted into the final energy spread. It corresponds to 90 degree rotation of the distribution of the muons in the beam in the energy-time phase space.
Phase rotation simulation 0 0 1 1 2 2 3 3 4 4 5 5 RF : 5MHz, 128kV/m RF : 5MHz, 250kV/m Δ E/E = 20MeV+12%-10% Δ E/E = 20MeV+4%-5%
Phase rotation simulation phase space Initial Phase 54.4 61.2 68.0 74.8 81.6MeV/c 54.4 61.2 68.0 74.8 81.6MeV/c Initial Phase After 1 turn After 1 turn After 2turns After 2 turns After 3turns After 3 turns After 4 turns After 4 turns After 5turns After 5 turns
Lattice Design In order to achieve a high intensity muon beam, it is necessary for the PRISM-FFAG to have both of large transverse acceptance and large momentum acceptance. Furthermore, long straight sections to install RF cavities are required to obtain a high surviving ratio of the muon. Therefore, the PRISM-FFAG requires its magnets to have large aperture and small opening angle. In such magnets, not only nonlinear effects but also fringing magnetic field are important to study the beam dynamics of FFAGs. Three-dimensional tracking is adopted to study the dynamics of FFAG from the beginning of the lattice design procedure. In this process, quasi-realistic 3D magnetic field maps, which are calculated applying spline interpolation to POISSON 2D field, were used instead of TOSCA field in order to estimate the optical property quickly
quasi-realistic 3D magnetic field r5 r4 r3 r2 r1 r x ( θ )
k=5 N=8 F/D = 7.1 r0=5m Comparison by tracking result
N=10 F/D=8 k=5 r0=6.5m 140000πmm mrad 3000πmm mrad 35000πmm mrad Tracking results
Layout of PRISM-FFAG Table 2: Present parameters of PRISM-FFAG No. of sectors 10 FFAG-Magnet Magnet type Radial sector DFD triplet Kicker Magnet C-shaped for Extraction Field index ( k -value) 4.6 F/D ratio 8.0 Opening angle F/2 : 2.2deg. D : 2.2deg. RF Cavity Kicker Magnet Half gap 17cm for Injection Maximum field Focus. : 0.24 Tesla Defocus. : 0.026 Tesla Average radius 6.5m for 68MeV/c RF AMP Tune horizontal : 2.69 vertical : 1.30 RF PS 5m
Features of PRISM-FFAG Magnet scaling radial sector intermediate pole Conventional type. Have larger circumference made of anisotropic magnet material. the ratio. magnet can have not only constant gap but triplet (DFD) also smaller fringing field. A scaling condition can be easy to fulfill. the intermediate pole F/D ratio can be tuneable. the field crump filters out local irregularity of the magnetic effects. large packing factor. the lattice functions field distribution. Thus the accuracy of the has mirror symmetry at the center of a straight pole shape is not necessary and the number section. of trim coils can be reduced. large aperture trim coils important for achieve a high intensity muon k value is tuneable. Therefore, not only beam. vertical tune and also horizontal tune are thin tuneable. Magnets have small opening angle. so FFAG has long straight section install RF cavities as mach as possible C-shaped
Magnet Design
Field Calculation 4000 10 r=580 cm F Componet 3500 9 r=600 cm D Componet r=620 cm 3000 8 r=640 cm r=660 cm 2500 7 k value + 1 B z (Gauss) r=680 cm 2000 6 r=700 cm r=720 cm 1500 5 z = 0 cm 1000 4 500 3 0 2 -500 1 -1000 0 0 2 4 6 8 10 12 14 16 18 580 600 620 640 660 680 700 720 � (Deg.) r (cm) 10 The 3D magnetic field was calculated by 9 using a 3D field calculation code, TOSCA. 8 These figure shows results of the calculation 7 of Bz as a function of θ (top), the local k F/D ratio 6 value (middle) and the F/D ration (bottom) as 5 a function of radius. The local k and F/D ratio 4 were calculated by the BL integration and 3 they are almost constant over the beam 2 region. Therefore, the scaling condition is 1 fulfilled. 0 580 600 620 640 660 680 700 720 r (cm)
Stray Field 100 Gauss 50 Gauss
” � “ ” “ ± RF System ultra-high field gradient Since the muon is an unstable particle (life Number of gap per cavity 5 time~2.2us), it is crucial to complete phase Length of cavity 1.75 m Number of core per gap 6 rotation as quickly as possible in order to Core material Magnetic Alloy increase a number of surviving muons. In Core shape Racetrack present design, PRISM requires very high Core size 1.4m × 1.0m × 3.5cm field gradient of 200kV/m at the low frequency Shunt impedance ∼ 159 Ω /core @ 5MHz (4-5 MHz). As compared with usual cavities, RF frequency 4 ∼ 5MHz PRISM has to operate its cavities at a Field gradient 200kV/m remarkably outstanding condition. Flux density in core 320 Gauss Tetrode 4CW150,000E Duty < 0.1% Proton Synchrotron RF System SATUNE Table 3: Parameters of PRISM-FFAG RF system. MIMAS 250 CERN PSB PRISM Cavity 200 CERN PS Field Gradient (kV/m) AGS J-PARC MA Cavities 150 ISIS (High Duty) KEK BSTR 100 KEK PS Ferrite Cavities J-PARC 50GeV MR 50 J-PARC 3GeV RCS 50GeV MR Upgrade 0 KEK-HGC 0 2 4 6 8 10 12 PRISM Frequency (MHz)
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